Full-Atom Cyclic Peptide Design via Test-Time Scaled Autoregressive Flow Matching

Cyclic peptides are an increasingly important therapeutic modality, offering antibody-like binding specificity within compact and chemically tunable scaffolds. Recent deep generative models have advanced target-specific peptide design, where SE(3)-equivariant diffusion and flow-matching frameworks provide natural inductive biases for peptide-protein complex generation. However, existing SE(3)-based peptide generators mainly focus on linear peptides and do not explicitly control cyclic topology. As shown by recent cyclic peptide benchmarks such as CPSea, current generative baselines still have limited cyclization success and remain weak at controllably generating disulfide- and isopeptide-cyclized peptide distributions. In this work, we propose CPFlow, a test-time scaled autoregressive flow-matching framework for receptor-conditioned cyclic peptide sequence-structure co-design. CPFlow autoregressively unmasks residues and predicts full-atom sequence-structure variables with continuous flow matching. By decomposing generation into stepwise flow updates, CPFlow allows each step to balance target binding with structural closure. At inference time, sequence-geometry guided unmasking and multi-particle test-time scaling explore high-confidence autoregressive trajectories beyond the trained model without additional training. Cyclization-aware relative position encodings further enable stable control over head-tail, disulfide, and isopeptide cyclization. Experiments on the CPSea benchmark show that CPFlow outperforms strong generative baselines across designability (scRMSD ↓ 0.30 Å), self-consistency (scRMSD ↓ 0.15 Å), and binding energy (mean ΔG ↓ 3.0), with 93.4% binding success and 0.623 diversity. The code for CPFlow is available at https://anonymous.4open.science/r/CPFlow-F226.